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Factor Analysis

Description: This quiz will test your knowledge of Factor Analysis, a statistical method used to identify the underlying structure of a set of variables.
Number of Questions: 14
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Tags: factor analysis statistics data analysis
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What is the primary goal of factor analysis?

  1. To identify the underlying structure of a set of variables

  2. To reduce the number of variables in a dataset

  3. To identify outliers in a dataset

  4. To create a predictive model

Show answer
Correct Option: A
Explanation:

Factor analysis is a statistical method used to identify the underlying structure of a set of variables. It is often used to reduce the number of variables in a dataset, but its primary goal is to identify the common factors that explain the relationships between the variables.

What is the difference between exploratory factor analysis (EFA) and confirmatory factor analysis (CFA)?

  1. EFA is used to identify the underlying structure of a set of variables, while CFA is used to test a specific hypothesis about the structure of the variables.

  2. EFA is used to reduce the number of variables in a dataset, while CFA is used to identify outliers in a dataset.

  3. EFA is used to create a predictive model, while CFA is used to identify the underlying structure of a set of variables.

  4. EFA is used to identify the common factors that explain the relationships between the variables, while CFA is used to test a specific hypothesis about the structure of the variables.

Show answer
Correct Option: A
Explanation:

Exploratory factor analysis (EFA) is used to identify the underlying structure of a set of variables without any prior assumptions about the structure. Confirmatory factor analysis (CFA) is used to test a specific hypothesis about the structure of the variables.

What is the scree plot in factor analysis?

  1. A plot of the eigenvalues of the correlation matrix of the variables

  2. A plot of the factor loadings of the variables

  3. A plot of the communalities of the variables

  4. A plot of the residuals of the factor analysis model

Show answer
Correct Option: A
Explanation:

The scree plot is a plot of the eigenvalues of the correlation matrix of the variables. It is used to determine the number of factors to extract in the factor analysis.

What is the purpose of factor rotation in factor analysis?

  1. To make the factor loadings easier to interpret

  2. To improve the goodness of fit of the factor analysis model

  3. To reduce the number of factors to extract

  4. To identify outliers in the dataset

Show answer
Correct Option: A
Explanation:

Factor rotation is used to make the factor loadings easier to interpret. It does not affect the goodness of fit of the factor analysis model or the number of factors to extract.

What is the most common factor extraction method in factor analysis?

  1. Principal components analysis (PCA)

  2. Maximum likelihood estimation (MLE)

  3. Generalized least squares (GLS)

  4. Weighted least squares (WLS)

Show answer
Correct Option: A
Explanation:

Principal components analysis (PCA) is the most common factor extraction method in factor analysis. It is a linear transformation that finds the directions of maximum variance in the data.

What is the difference between a factor loading and a communality in factor analysis?

  1. A factor loading is the correlation between a variable and a factor, while a communality is the proportion of variance in a variable that is explained by the factors.

  2. A factor loading is the regression coefficient of a variable on a factor, while a communality is the proportion of variance in a variable that is explained by the factors.

  3. A factor loading is the standardized regression coefficient of a variable on a factor, while a communality is the proportion of variance in a variable that is explained by the factors.

  4. A factor loading is the unstandardized regression coefficient of a variable on a factor, while a communality is the proportion of variance in a variable that is explained by the factors.

Show answer
Correct Option: A
Explanation:

A factor loading is the correlation between a variable and a factor. A communality is the proportion of variance in a variable that is explained by the factors.

What is the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy in factor analysis?

  1. A measure of the suitability of the data for factor analysis

  2. A measure of the goodness of fit of the factor analysis model

  3. A measure of the number of factors to extract

  4. A measure of the interpretability of the factor loadings

Show answer
Correct Option: A
Explanation:

The Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy is a measure of the suitability of the data for factor analysis. It ranges from 0 to 1, with values closer to 1 indicating that the data is more suitable for factor analysis.

What is the Bartlett's test of sphericity in factor analysis?

  1. A test of the hypothesis that the correlation matrix of the variables is an identity matrix

  2. A test of the hypothesis that the data is suitable for factor analysis

  3. A test of the hypothesis that the number of factors to extract is equal to the number of variables

  4. A test of the hypothesis that the factor loadings are all equal

Show answer
Correct Option: A
Explanation:

Bartlett's test of sphericity is a test of the hypothesis that the correlation matrix of the variables is an identity matrix. If the hypothesis is rejected, it indicates that the data is suitable for factor analysis.

What is the purpose of factor scores in factor analysis?

  1. To estimate the values of the factors for each observation

  2. To identify the underlying structure of the data

  3. To reduce the number of variables in the dataset

  4. To create a predictive model

Show answer
Correct Option: A
Explanation:

Factor scores are used to estimate the values of the factors for each observation. They can be used for a variety of purposes, such as clustering, discriminant analysis, and regression analysis.

What is the difference between a common factor and a specific factor in factor analysis?

  1. A common factor is a factor that is shared by all of the variables in the dataset, while a specific factor is a factor that is unique to a particular variable.

  2. A common factor is a factor that explains a large proportion of the variance in the data, while a specific factor is a factor that explains a small proportion of the variance in the data.

  3. A common factor is a factor that is correlated with all of the variables in the dataset, while a specific factor is a factor that is correlated with only a few of the variables in the dataset.

  4. A common factor is a factor that is extracted using principal components analysis, while a specific factor is a factor that is extracted using maximum likelihood estimation.

Show answer
Correct Option: A
Explanation:

A common factor is a factor that is shared by all of the variables in the dataset. A specific factor is a factor that is unique to a particular variable.

What is the purpose of a scree plot in factor analysis?

  1. To determine the number of factors to extract

  2. To identify the underlying structure of the data

  3. To reduce the number of variables in the dataset

  4. To create a predictive model

Show answer
Correct Option: A
Explanation:

A scree plot is used to determine the number of factors to extract in factor analysis. It is a plot of the eigenvalues of the correlation matrix of the variables. The number of factors to extract is typically determined by the point at which the scree plot begins to level off.

What is the difference between a factor loading and a communality in factor analysis?

  1. A factor loading is the correlation between a variable and a factor, while a communality is the proportion of variance in a variable that is explained by the factors.

  2. A factor loading is the regression coefficient of a variable on a factor, while a communality is the proportion of variance in a variable that is explained by the factors.

  3. A factor loading is the standardized regression coefficient of a variable on a factor, while a communality is the proportion of variance in a variable that is explained by the factors.

  4. A factor loading is the unstandardized regression coefficient of a variable on a factor, while a communality is the proportion of variance in a variable that is explained by the factors.

Show answer
Correct Option: A
Explanation:

A factor loading is the correlation between a variable and a factor. A communality is the proportion of variance in a variable that is explained by the factors.

What is the purpose of factor rotation in factor analysis?

  1. To make the factor loadings easier to interpret

  2. To improve the goodness of fit of the factor analysis model

  3. To reduce the number of factors to extract

  4. To identify outliers in the dataset

Show answer
Correct Option: A
Explanation:

Factor rotation is used to make the factor loadings easier to interpret. It does not affect the goodness of fit of the factor analysis model or the number of factors to extract.

What is the most common factor extraction method in factor analysis?

  1. Principal components analysis (PCA)

  2. Maximum likelihood estimation (MLE)

  3. Generalized least squares (GLS)

  4. Weighted least squares (WLS)

Show answer
Correct Option: A
Explanation:

Principal components analysis (PCA) is the most common factor extraction method in factor analysis. It is a linear transformation that finds the directions of maximum variance in the data.

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